发表机构
King Abdullah University of Science Technology; Lund University（阿卜杜拉国王科技大学; 隆德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出紧致度量图上高斯Whittle-Matérn场的桥表示，将场分解为图分量和边上的独立桥过程，从而提升似然评估、预测和模拟的效率与数值稳定性，并在芝加哥街道图和马德里交通数据上验证了其计算优势。
AI 中文摘要
高斯Whittle-Matérn场构成了一类在紧致度量图上的灵活高斯过程，其中空间依赖性通过分数阶随机偏微分方程由网络的几何和连通性所控制。本文针对半整数平滑参数情形（此时场具有马尔可夫性质）发展了这些场的一种新的桥表示。该表示将场分解为一个有限维图分量和各条边上的独立Whittle-Matérn桥过程。由此产生的分解导致了高效的似然评估、克里金预测和模拟方法。我们表明，与先前方法相比，这提高了数值稳定性并可以大幅减少计算时间。在芝加哥街道网络图上的模拟研究展示了采样方法的计算效率，而对马德里交通强度数据的应用则展示了基于似然的推断和预测的实际收益。这些方法已在R包MetricGraph中实现。
英文摘要
Gaussian Whittle-Matérn fields form a flexible class of Gaussian processes on compact metric graphs, where spatial dependence is governed by the geometry and connectivity of the network through a fractional-order stochastic partial differential equation. This paper develops a new bridge representation of these fields in the case of half-integer smoothness parameters, when the fields have Markov properties. This representation decomposes the field into a finite-dimensional graph component and independent Whittle-Matérn bridge processes on the individual edges. The resulting decomposition leads to efficient likelihood evaluation, kriging prediction, and simulation methods. We show that this improves numerical stability and can greatly reduce computation time compared to previous methods. A simulation study on a Chicago street-network graph illustrates the computational efficiency of the sampling method and an application to Madrid traffic intensity data demonstrates the practical gains for likelihood-based inference and prediction. The methods are implemented in the R package MetricGraph.
